A head covering with a band portion in a shape of a flat strip or loop and a plurality of flat members that are connected to or a part of the band is disclosed. The flat members projects toward a top side of the band. An outer surface of the flat members includes or is made of a material that can be fastened to a certain corresponding type of material. Thereby, the invention provides a foundation for hairpieces having a fastening component that corresponds to a fastening component used in the invention. The flat members as a whole generally cover a scalp of a head but not completely, exposing the scalp through gaps between flat members. Especially, a top portion or a crown of a scalp is generally exposed due to an open-top construction of the head covering. However, as a single hairpiece is fastened to multiple flat members, the hairpiece in turn works to hold the multiple flat members together. When more hairpieces are attached to flat members, the flat members become structurally solid in a shape that conforms to the contour of the scalp. In so doing, hairpieces cover and bridge the gaps between flat members, thereby completely covering a head.